Studies of time trends in cancer incidence and mortality have demonstrated that for most cancer sites, birth cohort exerts a stronger effect than year of diagnosis. These studies have also investigated some etiologic hypotheses, such as the effect of sunspot activity on malignant melanoma, and the age distribution of cancer. The age-period-cohort (APC) model has been used for these analyses by considering estimable functions of the parameters, avoiding the non-identifiability problem. This project will further develop the statistical methods for such analyses, and will apply these methods to data from selected cancer sites and selected geographic regions. The cancer sites are: lung, female breast, and malignant melanoma. Geographic regions are: Connecticut, Hawaii, Canada, Denmark, Finland, Israel, Japan, Norway, Sweden, U.K. and U.S. Estimable functions of the APC model parameters limits the summary to changes in trend, or curvature. This project will use other information, including theoretical models for carcinogenesis which specify the age distribution of cancer, as well as information on time trends in risk factors for cancer. Two models for carcinogenesis are to be used in this analysis, the multistage model and the two-stage model. This will assist in finding reasonable constraints that can be used in limiting the range of parameter estimates that can arise in the period and cohort effects due to the identifiability problem. In addition, it will increase understanding of the carcinogenesis process. Methodology will be developed to incorporate information on time trends in risk factors for cancer. The purpose of these models is to: (a) provide further information on the identifiability problem; (b) determine the extent to which these trends in risk factors can account for trends in the incidence rates; and, (c) assist in the monitoring of cancer risk and in forecasting future trends in cancer rates in the population. These models of cancer incidence will be used to develop and apply methods for forecasting trends in cancer. These forecasts will include estimates of summary rates, and the number of incident cases of cancer. The methods will incorporate information from epidemiological studies, providing a tool for planning cancer control strategies.